Abstract: Both direct and coincidence counting apparatus are described. The elimination of cosmic ray events by coincidence plus gamma ray shielding permits the reduction of counting rates far beyond that obtainable with shielding alone. By selection of materials and development of new components and techniques, the residual background count of beta counting equipment can be reduced to a very low value. Geiger counter equipment for routine laboratory measurements is described, have a background count of 0.7 c/m. Scintillation counters are shown to have a background of 0.2 c/m at 30% efficiency. A portable Geiger counter with a 3.7 c/m background is also described.